The defeated opposition candidate in Nigeria's presidential election, Muhammadu Buhari, on Wednesday alleged widespread vote irregularities, but urged calm following deadly riots.

"In the (Niger Delta region) and the southeast, there were no elections and our supporters weren't allowed to vote," the ex-military ruler told Voice of America radio's Hausa-language service.

He added however that "I urge people to calm down and be law-abiding as we are pursuing these irregularities with (the electoral commission) with a view to ensure justice for them."

President Goodluck Jonathan was on Monday declared winner with 57 per cent of the vote in polls, and many observers have lauded the conduct of the elections as a major step forward in a country with a history of ballot fraud.

Jonathan's victory sparked riots across Nigeria's north that left many dead, thousands displaced and hundreds wounded.

The vote exposed deep divisions in Africa's most populous nation. Jonathan is a southern Christian and Buhari is a Muslim from the north.